Boundary-Regulated Galactic Dynamics in Elastic Spacetime: Minimal Consistency Conditions for Rotation Curves and Weak Gravitational Lensing

ESSC v27 presents a structural reinterpretation of the audited 165-galaxy usable manifold derived from the original 175-galaxy SPARC-based source set after raw-point sufficiency reduction. The paper replaces an exact-core versus overlap emphasis with a fixed reduced atlas, a directed structural chain, and a role-based interpretation of center, radius, and circumference. The main empirical result is that outer persistence is best organized by transition-side baryonic support, which acts as the master axis of the persistent outer regime. Across the usable sample, the dominant structural chain is peak_f_baryon -> transition_y_raw -> transition_f_baryon -> raw_tail_y, and this chain leads to a classification of the manifold into five circular motion styles: closed_ring_main, stalled_before_circumference, vbar_diversion, inner_return, and ordinary_or_neutral. ESSC v27 does not propose a new force law or deny dark matter; its contribution is a structural interpretation of how the recovered galaxy manifold is organized into reproducible motion styles.